# Pipeline Analog-Digital Converters Dynamic Error Modeling for Calibration : Integral Nonlinearity Modeling, Pipeline ADC Calibration, Wireless Channel K-Factor Estimation

Sammanfattning: This thesis deals with the characterization, modeling and calibration of pipeline analog-digital converters (ADC)s. The integral nonlinearity (INL) is characterized, modeled and the model is used to design a post-correction block in order to compensate the imperfections of the ADC. The INL model is divided into: a dynamic term designed by the low code frequency (LCF) component depending on the output code k and the frequency under test m, and a static term known as high code frequency (HCF) component depending solely on the output code k. The HCF is related to the pipeline ADC circuitry. A set of adjacent piecewise linear segments is used to model the HCF. The LCF is the dynamic term depending on the input signal characteristics, and is modeled using a polynomial with frequency dependent coefficients. Two dynamic calibration methodologies are developed to compensate the imperfections of the pipeline ADC. In the first approach, the INL model at hand is transformed into a post-correction scheme. Regarding the HCF model, a set of gains and offsets is used to reconstruct the HCF segments structure. The LCF polynomial frequency dependent coefficients are used to design a bank of FIR filters which reconstructs the LCF model. A calibration block made by the combination of static gains/offsets and a bank of FIR filters is built to create the correction term to calibrate the ADC. In the second approach, the calibration (and modeling) process is extended to the upper Nyquist bands of the ADC. The HCF is used directly in calibration as a look-up-table (LUT). The LCF part is still represented by a frequency dependent polynomial of which the coefficients are used to develop a filter bank, implemented in the frequency domain with an overlap-and-add structure. In brief the calibration process is done by the combination of a static LUT and a bank of frequency domain filters. The maximum likelihood (ML) method is used to estimate the K-factor of a wireless Ricean channel. The K-factor is one of the main characteristics of a telecommunication channel. However, a closed-form ML estimator of the Kfactor is unfeasible due to the complexity of the Ricean pdf. In order to overcome this limitation, an approximation (for high K-factor values) is induced to the Ricean pdf. A closed-form approximate ML (AML) for the Ricean K-factor is computed. A bias study is performed on the AML and the bias derived value is used to improve the AML estimation, leading to a closed-form bias compensated estimator (BCE). The BCE performance (in terms of variance, bias and mean square error (MSE)) is simulated and compared to the best known closed-form moment-based estimator found in the literature. The BCE turns to have a superior performance for low number of samples and/or high K-factor values. Finally, the BCE is applied on real site wireless channel measurements in an urban macro cell area, using a 4-antenna transmit/receive MIMO system.

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